Certainly coming from East Anglia (and c-w-s should really be thankful the announcements aren't in a Norfolk accent, or there'd be a particular problem with Shadwell and Poplar would really grate), LCY is much easier for both arrivals and departures - 15 minutes from Stratford for trains to-and-from Norwich, meaning I can catch a train after work and very comfortably make the last DUB flight of the day with the added bonus of avoiding the nightmare that is Holborn station in rush hour.
Arriving, I can be halfway home long before I've even made it as far as the Underground at LHR, let alone the journey across to Liverpool Street.
I haven't bothered to time the doors opening to DLR platform, but I know the last time I did it - on an LX flight from ZRH, so also involving immigration - I was at Bank in just over 30 minutes. With a 22 minute journey time on the DLR, and a minute's wait on the platform IIRC, that's nine minutes including immigration. I reckon you could comfortably do seven on a domestic.